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Isotropic line, the Glossary

Index Isotropic line

In the geometry of quadratic forms, an isotropic line or null line is a line for which the quadratic form applied to the displacement vector between any pair of its points is zero.[1]

Table of Contents

  1. 28 relations: Élie Cartan, Circular points at infinity, Complex geometry, Complex projective plane, Coral Gables, Florida, Definite quadratic form, Differential equation, Differential geometry of surfaces, Dover Publications, Edmond Laguerre, Emil Artin, Encyclopedia of Mathematics, Geodesic, Homogeneous coordinates, Imaginary unit, Internet Archive, Isotropic quadratic form, Light cone, Line (geometry), Multivector, Null vector, O. Timothy O'Meara, Photon, Quadratic form, Spinors in three dimensions, University of Miami, W. H. Freeman and Company, World line.

Élie Cartan

Élie Joseph Cartan (9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry.

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Circular points at infinity

In projective geometry, the circular points at infinity (also called cyclic points or isotropic points) are two special points at infinity in the complex projective plane that are contained in the complexification of every real circle.

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Complex geometry

In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers.

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Complex projective plane

In mathematics, the complex projective plane, usually denoted P2(C) or CP2, is the two-dimensional complex projective space.

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Coral Gables, Florida

Coral Gables is a city in Miami-Dade County, Florida, United States.

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Definite quadratic form

In mathematics, a definite quadratic form is a quadratic form over some real vector space that has the same sign (always positive or always negative) for every non-zero vector of. Isotropic line and definite quadratic form are quadratic forms.

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Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.

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Differential geometry of surfaces

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric.

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Dover Publications

Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker.

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Edmond Laguerre

Edmond Nicolas Laguerre (9 April 1834, Bar-le-Duc – 14 August 1886, Bar-le-Duc) was a French mathematician and a member of the Académie des sciences (1885).

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Emil Artin

Emil Artin (March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent.

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Encyclopedia of Mathematics

The Encyclopedia of Mathematics (also EOM and formerly Encyclopaedia of Mathematics) is a large reference work in mathematics.

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Geodesic

In geometry, a geodesic is a curve representing in some sense the shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold.

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Homogeneous coordinates

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry.

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Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication.

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Internet Archive

The Internet Archive is an American nonprofit digital library founded in 1996 by Brewster Kahle.

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Isotropic quadratic form

In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero. Isotropic line and isotropic quadratic form are quadratic forms.

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Light cone

In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime. Isotropic line and light cone are theory of relativity.

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Line (geometry)

In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light.

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Multivector

In multilinear algebra, a multivector, sometimes called Clifford number or multor, is an element of the exterior algebra of a vector space.

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Null vector

In mathematics, given a vector space X with an associated quadratic form q, written, a null vector or isotropic vector is a non-zero element x of X for which. Isotropic line and null vector are quadratic forms.

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O. Timothy O'Meara

Onorato Timothy O'Meara (January 29, 1928 – June 17, 2018) was an American mathematician known for his work in number theory, linear groups and quadratic forms.

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Photon

A photon is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force.

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Quadratic form

In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). Isotropic line and quadratic form are quadratic forms.

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Spinors in three dimensions

In mathematics, the spinor concept as specialised to three dimensions can be treated by means of the traditional notions of dot product and cross product.

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University of Miami

The University of Miami (UM, UMiami, Miami, U of M, and The U) is a private research university in Coral Gables, Florida.

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W. H. Freeman and Company

W.

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World line

The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. Isotropic line and world line are theory of relativity.

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References

[1] https://en.wikipedia.org/wiki/Isotropic_line

Also known as Null line.